In telecommunications, diversity is a property often searched for improving a reliability of a signal transmission. This is particularly true in wireless communications where a signal transmission is affected by fading, co-channel interference, thermal noise and/or error bursts. Communication schemes providing diversity, called diversity schemes in the following, are based on the assumption that individual communication channels experience different impairments. Several copies of a same signal may be therefore transmitted on and/or received from a plurality of communication channels, hoping that each copy is differently affected by the communication channel impairments. One objective is to obtain on a receiver side, by a combination of the received copies, a good reconstruction of information words comprised in the transmitted signal.
The telecommunication literature is rich of several types of diversity schemes. We can mention for instance:                Diversity schemes based on time diversity in which multiple versions of a same signal are transmitted at different time instants.        Diversity schemes based on frequency diversity in which a signal is transmitted using several frequencies or spread over a wide spectrum that is affected by frequency-selective fading.        Diversity schemes based on space diversity in which a signal is transmitted over several different propagation paths. In the case of wireless transmission, it can be achieved by antenna diversity using multiple transmitter antennas (transmit diversity) and/or multiple receiving antennas (reception diversity), or both.        Diversity schemes based on polarization diversity in which multiple versions of a signal are transmitted and received via antennas with different polarization.        
Space Time Codes (STC) (respectively Space Frequency Codes (SFC)) are examples of diversity schemes offering jointly spatial and temporal diversity (resp. spatial and frequency diversity) in which reliability of wireless transmission is improved by using a plurality of transmit antennas.
An evolution of STC (resp. SFC) codes are the Space Time Block Codes (STBC) (resp. Space Frequency Block Codes (SFBC)) in which a data stream to be transmitted is encoded in blocks, which are distributed among spaced antennas and across time (resp. across frequencies).
An STBC (resp. SFBC) code is usually represented by a matrix.
      (                                        S            11                                    …                                      S                          1              ⁢              K                                                            ⋮                          ⋱                          ⋮                                                  S                          L              ⁢                                                          ⁢              1                                                …                                      S            LK                                )     where the Sij(i ∈ [1; L], j ∈ [1; K]) are linear combination of symbols to be transmitted on a time slot i (resp. on a frequency i) from antenna j.
A popular STBC code adapted to transmission devices having two transmit antennas (or an even number of transmit antennas) and an arbitrary number of receive antennas was proposed by Siavash Alamouti et al. in the document “Space-time codes for high data rate wireless communication: Performance analysis and code construction./IEEE Transactions on Information Theory 44 (2): 744-765 ” with the following 2×2 matrix:
      Q    ⁡          (      x      )        =            [                                                  S              11                                                          S              12                                                                          S              21                                                          S              22                                          ]        =          [                                                  x              1                                                          x              2                                                                          -                              x                2                *                                                                        x              1              *                                          ]      where * denotes complex conjugate.
The matrix of Alamouti (or Alamouti Matrix) generates four output symbols x1, x2, −x2*, and x1*, from two input symbols x1 and x2, x1 being transmitted on a first time slot (resp. on a first frequency) and a first antenna, x2 being transmitted on the first time slot (resp. on the first frequency) and a second antenna, −x2* being transmitted on a second time slot (resp. on a second frequency) and the first antenna, x1* being transmitted on the second time slot (resp. on the second frequency) and the second antenna.
A further evolution of STBC codes (resp. SFBC codes) are Differential Space Time Block Codes (DSTBC) (resp. Space Frequency Block Codes (DSFBC)). DSTBC codes (resp. DSFBC codes) involve a differential encoding of symbols. The differential encoding allows, at a receiver, to avoid an estimation of phases of channel coefficients. This is particularly interesting when a channel has a small coherence time with respect to a time symbol period.
Even if generalizations of the STC (resp. SFC) codes based on the Alamouti matrix exist in the literature with larger matrices adapted to more than two antennas and more than two time slots (resp. more than two frequencies), the original 2×2 matrix of Alamouti remains commonly used. This matrix limits the number of symbols that can be inputted to the STC (STBC or DSTBC) (resp. SFC (SFBC or DSFBC)) coder to two symbols at a time.
Since, generally, inputs of a communication system are not symbols, but vectors of symbols, a plurality of STC (resp. SFC) coders based on the Alamouti 2×2 matrix (called Alamouti STC (resp. SFC) coders in the following) are parallelized to encode each vector. For instance, with vectors of symbols of size m, a set of m/2 Alamouti STC (resp. SFC) coders are used to encode the symbols of each vector of symbols.
Generally the symbols of each vector of symbols are interleaved by an interleaving module positioned before the set of STC (respectively SFC) coders, which creates a first level of diversity by dispatching the symbols on different time or frequency resources associated with different impairments.
Linear pre-coding is another method that can be used to increase the (time, frequency and/or in space) diversity in a transmitted signal in systems with a small number of antennas. A linear pre-coder, based for instance on cyclotomic rotations, creates linear combinations of n input symbols and spreads m output symbols resulting from the linear combinations over different transmission resources. Such linear pre-coder can achieve a diversity increase by a factor n.
Linear pre-coding can also be used for other purposes, for instance to decrease a PAPR (Peak-to-Average Power Ratio) of an OFDM (Orthogonal frequency-division multiplexing) modulation by using a Discrete Fourier Transform (DFT) before mapping the so pre-coded symbols on the sub-carriers of the OFDM modulation, or to apply a multi-user interference mitigation technique by using the spatial dimensionality of a multi-user MIMO (Multiple Input Multiple Output) system.
Known transmission devices comprise an interleaving module and a module comprising a set of parallel STC (resp. SFC) coders. In the following, a module combining an interleaving module and a module comprising a set of parallel STC (resp. SFC) coders (called signal encoding module in the following) is called a diversity creation module. A diversity creation module can also comprise a linear pre-coding (LPC) module positioned before the interleaving module and the signal encoding module. The diversity creation module benefits of properties brought by the modules constituting it.
For instance a diversity creation module can benefit of a first level of diversity brought by an LPC module, a second level of diversity brought by an interleaving module and a third level of diversity brought by a signal encoding module.
In a transmission device, as already mentioned, a diversity creation module receives generally vectors of symbols in which symbols are modulated symbols generated by a modulation module such as, for example, a Bit Interleaved Coded Modulation (BICM) module, from information words. The diversity creation module then generates tuples of transmission symbols from the vector of modulated symbols. In the case of parallel Alamouti STC (resp. SFC) coders, each Alamouti STC (resp. SFC) coder generates a quadruple of transmission symbols from a pair of input symbols representative of the modulated symbols. Indeed, when the signal encoding module is preceded only by the interleaving module, the symbols representative of the modulated symbols are the modulated symbols themselves, while when the signal encoding module is preceded by an LPC module and an interleaving module, the symbols representative of the modulated symbols are combined symbols resulting from the linear combination performed by the LPC module.
Each transmission symbol is transmitted on an associated transmission channel different for each transmission symbol. Each transmission channel is provided by a dedicated transmission resource. A transmission resource is generally defined by an antenna of a plurality of antennas available on the transmission device, a time slot (resp. a frequency) of a set of pre-defined time slots (resp. pre-defined frequencies) and a sub-carrier of a set of pre-defined sub-carriers. The selection of the antenna and the time-slot (resp. the frequency) allocated to a transmission symbol is fixed by the 2×2 Alamouti matrix. A different sub-carrier is then allocated to each Alamouti STC coder. In the case of SFC coders, a different set of sub-carriers is then allocated to each Alamouti SFC coder.
On a receiver device, a transmitted signal is received in the form of vectors of observations. Each observation corresponds to a transmission symbol impacted by the associated transmission channel and affected by a noise corresponding to the associated transmission channel. The receiver device comprises an inverse diversity creation module which corresponds to the diversity creation module of the transmission device.
The inverse diversity creation module comprises a signal decoding module comprising inverse STC (resp. SFC) modules corresponding to the STC (resp. SFC) coders comprised in the signal encoding module of the transmission device. The inverse diversity creation module is able to generate a vector of processed observations from a vector of observations. Each processed observation of a vector of processed observations corresponds to a modulated symbol of a vector of modulated symbols processed by the diversity creation module.
One objective of the receiver device is to reconstruct decoded information words as close as possible to information words transmitted into the vector of transmission symbols. Many receiver devices use a reconstruction process based on computations of likelihood.